A Wilkinson power divider with harmonic suppression through low-pass filter for GSM and LTE applications

Conventional Wilkinson power dividers (WPDs) perform satisfactorily near the intended operation frequency. Nonetheless, these WPDs demonstrate subpar performance in the stopband and necessitate a significant physical space. To enhance the existing level of advancement and in order to improve on the current state-of-the-art, a modified WPD is designed and fabricated, demonstrating a significant improvement in stopband and superior isolation between output ports. To improve the stopband and suppress unwanted harmonics, a low-pass filter (LPF) structure is placed in the both branches of the conventional WPD. The proposed modified WPD depicts a wide stopband bandwidth (fSB > 17.25 GHz) from 2.75 to over 20 GHz with an attenuation level of 20 dB, suppressing 2nd to 11th harmonics. According to measured results, the input return loss (|S11|), insertion loss (|S21|) and output isolation (|S32|) at f = 1.8 GHz are better than 33 dB, 3.2 dB and 21 dB, respectively. Indeed, the proposed modified WPD exhibits a magnitude imbalance of 0.00018, a phase imbalance of 1.25 degrees and a group delay of 0.5 ns. The proposed WPD depicts a compact size of 35 mm × 25 mm (0.38 λg × 0.27 λg), where λg is the guided wavelength at f = 1.8 GHz. There is a good agreement between the simulated and measured results. According to the obtained results, the proposed modified WPD shows a desirable performance for modern LTE and GSM communication applications.


Power divider structure design
The WPD design methodology is depicted in Fig. 1.The aim is to design a modified WPD with a compact size, high isolation, ultra-wide rejection band and high suppression factor.In the first step, a conventional WPD is designed and simulated.A basic LC resonator is designed based on normalisation coefficients of the third-order LPF circuit and mathematical analysis 45 in the second step.The roll-off-rate (ROR) is one of the important performance parameters for the LPF structures, which shows the changing rate from the passband to the stopband.A novel resonator is designed to improve the LPF response (sharpen ROR parameter) compared to the basic resonator.A novel harmonic suppression is presented and analysed in the fourth design step.The proposed novel harmonic suppression is used to achieve a wide stopband and suppress unwanted harmonics.Then, the novel harmonic suppression structure is added to the proposed novel modified resonator to create an LPF structure.In the final step, the proposed LPF structure is replaced in the both branches of conventional WPD to pass DC frequency signal and fundamental harmonic and eliminate other harmonics (2nd to 11th harmonics).Placing filters within the branches of a WPD can offer several advantages, but it is important to justify this design choice based on specific requirements and constraints.Several potential advantages and justifications of employing LPF structures in the WPD branches are size mitigation, reducing signal path length and improving isolation between output ports.However, it is important to note that the choice to integrate filters within the power divider branches should be made after considering the specific requirements of the application, including frequency range, desired filter characteristics, size constraints, and performance goals.
A conventional WPD is designed with two-quarter wavelength (λ/4) microstrip transmission lines with the impedance of each branch 70.71 Ω ( Z 0 √ 2andZ 0 = 50 ), and a resistance of 100 Ω (R = 2 Z 0 �) which is placed between the two output ports.A schematic for the block diagram and simulation results of the proposed conventional WPD at f = 1.8 GHz is shown in Fig. 2a.According to Fig. 2b, the proposed conventional WPD shows a well performance for the input return loss (S 11 ), isolation (S 32 ) and insertion loss (S 21 ) at f = 1.8 GHz. Figure 3, depicts a high-frequency harmonic balance analysis from 0 to 20 GHz.According to Fig. 3, the magnitude of the harmonic balance is very close to -3 dBm for an input power P IN = 0 dBm.In the following, an LPF structure will be designed in order to improve the WPD features such as suppressing unwanted harmonics, high isolation, wider stopband bandwidth and compact size.

LPF design methodology
In the first stage of LPF design, a simple LPF resonator is designed based on the normalisation coefficients of the third-order LPF circuit and mathematical analysis 45 .
In the above Eqs.(1.a) and (1.b), Z 0 is the characteristic impedance of the transmission line, which is equal to 50 Ω.f c is a − 3 dB cut-off frequency, g Ci and g Li are the normalisation coefficients of the LPF circuit.From 45 , the normalisation coefficients of the LPF circuit are g L1 = 1.130, g L2 = 0.2559, g C2 = 1.138, and g L3 = 1.360.Using Eqs.(1.a) and (1.b), an LPF resonator is designed for f c = 2.7 GHz.In Fig. 4, the circuit diagram of the designed filter can be seen along with the shape of its response.In Fig. 4a, the value of L a = 3.3 nH, L b = 0.75 nH, L c = 4 nH and C a = 1.34 pF.According to Fig. 4b, the transmission zero ( T Z ) can be calculated by Eq. (2).In Fig. 4b, |T z1 |= 92 dB (at f Tz1 = 5.02 GHz).
In the following, using Eqs.(1.a)According to Fig. 5b, the ROR is 13.65 dB/GHz for the conventional resonator and|T z2 |= 49 dB (at f Tz1 = 4.534 GHz).To improve the ROR and achieve a sharp response, two conventional resonator are placed in series, shown in Fig. 6.The dimension for the modified resonator #1 (shown in Fig. 6a) are g = 5.9 mm, h = 13.2 mm, i = 7.5 mm, j = 3.5 mm, k = 7 mm and l = 1 mm.
Aiming for a higher Roll-of-rate (ROR), the conventional resonator was modified.These modifications manipulate the distributed surface current and electrical field and improves the frequency response of the conventional   www.nature.com/scientificreports/resonator 44 .The new design structure illustrates better response (sharper ROR and higher SF) than the previous structure.According to Fig. 6b, the new resonator (shown in Fig. 6a) shows a sharp ROR = 23.5 dB/GHz and two transmission zeros; |T z3 |= 74 dB (at f Tz3 = 4.02 GHz) and |T z4 |= 70 dB (at f Tz4 = 4.583 GHz), respectively.In the following, a much better response (sharper ROR and more T zs ) is obtained by making changes in the resonator structure.Figure 7 displays the suggested alteration in the structure of resonator #2 along with the corresponding simulated outcomes.As depicted in Figure 7b, the modified resonator #2 exhibits a more pronounced response when contrasted with modified resonator #1.Additionally, the return loss of modified resonator #2 displays an improved response and a broader resonance range compared to modified resonator #1.Furthermore, the overall size of modified resonator #2 has been notably decreased in comparison to the dimensions of modified resonator #1.This reduction in size not only lowers construction costs but also results in a smaller final design.
According to the Fig. 8b To achieve an accurate LC equivalent circuit, the meandering lines in the layout of the modified resonator have been modelled by a π-type circuit according to the reference 44 .Apart from the modelling approach used here, there are other techniques based on modal analysis 46 , artificial intelligence-based approaches 47 and transfer functions 48,49 .According to the obtained results, there is a good agreement between the simulated results for the layout and LC equivalent circuit.
According to Fig. 8b, the proposed modified resonator illustrates a sharp response (ROR = 175 dB/GHz) and frequency selection (four T zs ), but the stopband bandwidth is weak.Harmonic suppression structures to control unwanted frequencies are necessary to improve the rejection bandwidth.The proposed harmonic suppression structure consists of four suppression cells; each suppresses a frequency range in the rejection band.Fig. 9 shows the schematic circuit of the first suppression cell, simulated results and layout.According to Fig. 9b    A suppression structure (four harmonic suppressor cells) have been added to the modified LPF resonator to achieve a large stopband and improve the frequency response in the rejection band.According to obtained results, good agreements are observed between the layout and LC circuit results.The introduction of the suppressor cells to the modified LPF resonator yields an LPF structure with a sharp response and large stopband as depicted in Fig. 13.The final structure of the LPF structure, simulated results and measured results are shown in Fig. 13.Table 1 shows a comparison between the simulated results for the proposed LPF structure and recent state-of-the-art.According to Fig. 13b, the-3 dB cut-off frequency for the proposed LPF structure is 2.69 GHz.The proposed LPF structure illustrates a sharp ROR parameter and equal to 180 dB/GHz.The return loss (RL) and insertion loss (IL) in the passband and stopband are better than 19, 0.53, 0.56 and 20 dB, respectively.The suppression level in the rejection band is better than 20 dB leading to SF parameter being 2. The proposed LPF structure shows an ultra-wide stopband bandwidth which covers a 17.31 GHz range (from 2.69 to over 20 GHz), with an RSB of 1.79 having been obtained.
The proposed structure has ROR and RSB better than previous works introduced in Table 1.Also, the dimensions of the structure are better than [9][10][11] .
To validate the concept of the design methodology, the proposed LPF structure is subjected to simulation at two distinct frequency bands to showcase its performance in both the passband and the stopband.Fig. 14 illustrates the simulation results of the surface current distribution for the proposed LPF structure.As depicted in Fig. 14a, at a frequency of 1.8 GHz, which falls within the passband region of the LPF, the surface current flows towards port 2, clearly indicating the passband operation.In Fig. 14b, at a frequency of 3.17 GHz within the stopband, the LPF structure effectively blocks the signal and surface current.

Proposed WPD
The proposed LPF structure is integrated into both branches of conventional WPD to improve the stopband bandwidth, suppress unwanted harmonics and increase the isolation between output ports.The schematic of the final layout of the proposed modified WPD and simulated results are depicted in Fig. 15.
According to Fig. 15b, the simulated results of the proposed modified WPD illustrate an ultra-wide stopband up to 40 GHz with a 20 dB attenuation level.According to simulated results in Fig. 15b, above 20 GHz, the S 11 loss increases which can be attributed to several high frequency loss sources such as material losses (dielectric losses, conductor losses and parasitic components), impedance mismatches and radiation losses from transmission lines and components.Fig. 16 shows the imbalance EM analysis that depicts the simulation results of the group delay, phase difference and magnitude difference between the two outputs.According to the results, the group delay, phase and magnitude imbalance are better than 0.5 ns ,0.15 degrees and 0.00018 at f = 1.8 GHz, respectively, this discrepancy in output power levels can be attributed to simulation inaccuracies and a slight    variation of 0.001 mm in the overall design.It could also arise from an asymmetrical positioning with a modeling difference of approximately 0.001 mm.Fig. 17 shows the simulated results of harmonic balance analysis (with P IN = 0 dBm at f = 1.8 GHz) for the conventional WPD and the proposed modified WPD.To simulate the harmonics, the harmonic balance simulation in ADS software was used.It is important to note that even in passive devices like Wilkinson Power Dividers (WPDs), the generation of undesired harmonics can occur for various reasons.These reasons include impedance mismatches at the input or output ports, the presence of non-ideal components (such as non-linear parasitic capacitance and inductance in high-frequency resistance models), and crosstalk between different branches, which can result in signal reflections within the WPD and the subsequent generation of unwanted harmonics.The fundamental frequency (f = f 0 ) is located in the passband of the proposed LPF structure, therefore, the output magnitude remains constant and equals 3 dBm for both conventional and modified WPDs.According to Fig. 17a, other harmonics (2nd to 11th) are located in the stopband of the LPF structure that are suppressed significantly.

Results and discussion
The proposed modified WPD is implemented on the Rogers RO4003c substrate with a dielectric constant of   2 shows a comparison between the obtained results for the proposed modified WPD and other works described in the literature.
Among power dividers, WPDs are widely used due to their simple construction, narrow bandwidth, and reliable performance.WPDs can be used in test systems to measure two different characteristics of a signal, such as frequency and power, for broadband-independent signal sampling.GSM modems have a wide range of applications in transaction terminals, supply chain management, and security applications.One of the frequently used frequency bands in GSM is the 1800 MHz range, known for its widespread availability and well-established presence within GSM networks 44 .The proposed WPD shows desirable performance at this frequency, in terms of having a wide stop band, high isolation, and suppression of unwanted harmonics.The proposed WPD is versatile and finds application in various scenarios, including distributing power to antennas in an array, partitioning power among different components within a system, and aggregating power from various system segments.Moreover, the presented WPD is suitable for use in devices like radio receivers and transmitters, as well as more advanced systems found in the telecommunications and commercial sectors.

Figure 1 .
Figure 1.The design procedure of the proposed WPD.
(3.a) and (3.b), schematic circuits are converted into the layout structure.The values of the inductors and capacitors of the third-order circuit can be obtained using Eqs.(1.a) and (1.b).In addition, the physical lengths of the low-and high-impedance lines are calculated using Eqs.(3.a) and (3.b).

Figure 13 .
Figure 13.Proposed LPF (a) Layout.(b) Simulation results from 0 to 50 GHz.(c) Experimental setup.(d) S 21 simulated and measured results up to 20 GHz.The values of L 16 = 25 mm and W 17 = 9.8 mm.

Figure 16 .
Figure 16.(a) Simulation results of Group delay.(b) Simulation results of Magnitude and phase imbalance for the proposed WPD.
3.38, a thickness of 0.8 mm, and a loss tangent of 0.0022.An AGILENT/HP N9918A Vector Network Analyzer was used to measure the S-parameters response with a frequency range of 0.1-20 GHz.The fabricated sample of the presented modified WPD and experimental/measurement setup are shown in Fig.18.The simulated and measured results are shown in Fig.19.According to Fig.19d,e, the reasons for the structural imbalance include manufacturing and assembly errors of SMA connectors, as well as measurement errors by VNA and cables.According to the measured results, the isolation between output ports (|S 32 |), insertion loss (|S 21 ) and input return loss (|S 11 |) are better than 21.2 dB, 3.52 dB and 33.2 dB, respectively, at f = 1.8 GHz.There is a good agreement between simulated and measured results.According to the results, the proposed WPD shows a wide stopband from 2.7 to 40 GHz and 2.7 to 20 GHz with 20 dB attenuation levels for both the simulated and measured results, respectively.
Figure 20 shows the stopband bandwidth and harmonic suppression level for the proposed modified WPD.The second to eleventh harmonics at frequencies 2f 0 to 11f 0 (f 0 = 1.8 GHz) are depicted to be suppressed with better than −40.85, −22.48, −32.91, −50.47, −42.68, −47.66, −46.55, −32.88, −23.61 and −29.91 (all in dB) attenuation levels.Compared with the state-of-the-art WPDs, desirable suppression levels in the stopband are illustrated for the modified WPD and harmonics have been significantly attenuated in this region.Table

Figure 20 .
Figure 20.Harmonic suppression, simulation and measurement results of proposed conventional and modified WPDs.

Table 1 .
Comparison between simulated results and other studies for the LPF structure.

Table 2 .
Comparison of the proposed modified WPD with related previous works.